Lesson 4
1. Lesson 4
1.10. Connect
Module 3: Quadratics
Connect
Lesson Assessment
Complete the Lesson 4 Assignment that you saved to your course folder.
Going Beyond
You learned in this lesson how to convert the vertex form of the quadratic function to the standard form of the quadratic function y = ax2 + bx + c by squaring the binomial, clearing the brackets, and collecting like terms. You can do the reverse, converting the standard form of the quadratic function to the vertex form by completing the square.
For example, follow these steps.
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This is the standard form. |
y = 2x2 − 8x + 30 |
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Group the first two terms. Factor out the leading coefficient if a ≠ 1. |
y = 2(x2 − 4x) + 30 |
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Take half the coefficient of the x-term, and square it. |
y = 2(x2 − 4x + 4 − 4) + 30 |
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Add the squared value, and subtract it from the first two terms. |
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Group the first three terms: they form a perfect square trinomial. |
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Rewrite the perfect square trinomial as the square of a binomial. |
y = 2(x − 2)2 − 8 + 30 |
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This is the vertex form. |
y = 2(x − 2)2 + 22 |
One reason to convert the standard form to the vertex form is that in the vertex form, values of h and k give the coordinates of the vertex of the parabola. The value of h is also the x-coordinate of the axis of symmetry of the parabola.
Go back to Try This 2, where you know both forms, and convert Chris’s and Jean-Guy’s standard forms back to their vertex forms by completing the squares.